Multi-factorial, polygenic and quantitative traits are ubiquitous and include complex diseases in humans (e.g., cardiovascular disease, diabetes, hypertension), traits of economic importance in livestock (growth, milk production, meat quality, disease resistance) and plants (yields, disease resistance), as well as models for human disease in experimental animal populations (mice) and farm animals (swine). Statistical gene mapping is one of few promising avenues for advancing our knowledge of the genetic architecture and molecular basis of multi-factorial traits. Two major steps are required to improve the accuracy and power of gene mapping: The development of statistical methods for joint linkage disequilibrium and linkage mapping for fine-mapping and genome scanning, and the implementation of such methods with efficient computing algorithms, in particular with efficient multi-locus genotype samplers, which enable the analysis of large, multi-generational, complex pedigrees. The goal of this project is to develop, implement, evaluate and compare statistical methods for joint linkage disequilibrium and linkage mapping of genes affecting multi-factorial or quantitative traits in outbred, pedigreed populations (mainly farm animal and human populations). The best method(s) will be made available in a set of computer programs, which extend considerably the range of pedigrees, which can be analyzed, or ideally, which can handle every pedigree used in gene mapping projects. An approximate variance components or expectation method for joint linkage disequilibrium and linkage mapping of quantitative trait loci will be further developed and implemented. A fully parametric or distribution Bayesian analysis for joint linkage disequilibrium and linkage mapping of QTL will be developed. These methods will be compared with simulated data, representing different population structures, histories and genetic marker types, and with real data.